Conformally invariant trilinear forms on the sphere

To each complex number λ is associated a representation πλ of the conformal group SO0(1, n) on C∞(Sn−1) (spherical principal series). For three values λ1, λ2, λ3, we construct a trilinear form on C∞(Sn−1)×C∞(Sn−1)×C∞(Sn−1), which is invariant by πλ1 ⊗πλ2 ⊗ πλ3 . The trilinear form, first defined for (λ1, λ2, λ3) in an open set of C is extended meromorphically, with simple poles located in an explicit family of hyperplanes. For generic values of the parameters, we prove uniqueness of trilinear invariant forms. 02000 Mathematics Subject Classification : 22E45, 43A85